What is 100(2pif(40(10^{-6}))) ?

The solution to 100(2pif(40(10^{-6}))) is (pif)/(125)

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simplify 100(2pif(40(10^{-6})))

simplify

100 (2 π f (40 (1 0^{- 6})))

\frac{π f}{125}

Solution steps

100 (2 π f (40 (1 0^{- 6})))

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= 100 \cdot 2 \cdot 40 π \frac{1}{1 0 ^{6}} f

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot 100 \cdot 2 π f \cdot 40}{1 0 ^{6}}

Multiply the numbers:

1 \cdot 100 \cdot 2 \cdot 40 = 8000

= \frac{8000 π f}{1 0 ^{6}}

Factor

8000 : 2^{6} \cdot 5^{3}

Factor

1 0^{6} : 2^{6} \cdot 5^{6}

= \frac{2 ^{6} \cdot 5 ^{3} π f}{2 ^{6} \cdot 5 ^{6}}

Cancel

\frac{2 ^{6} \cdot 5 ^{3} π f}{2 ^{6} \cdot 5 ^{6}} : \frac{π f}{5 ^{3}}

= \frac{π f}{5 ^{3}}

5^{3} = 125

= \frac{π f}{125}

x^{2} (x - 6)^{2}

e^{x t} e^{y t} e^{z t}

(\frac{π ^{2}}{4})^{- \frac{1}{4}}

7.88 e^{- 0.05 \cdot \frac{1}{2}}

e^{5 y} \cdot 5 \cdot e^{5 y}

What is 100(2pif(40(10^{-6}))) ?
The solution to 100(2pif(40(10^{-6}))) is (pif)/(125)